The Kentucky Legislature elected Henry Clay to the Senate even though he was 29 years old, under the age of 30. It would be interesting if AOC were elected VP at 32.
Well, Clay's ineligibility when he was first elected to the Senate wasn't overlooked (& unconstitutionally so, I might add) so much as nobody knew of Clay's age, not to mention that during that period Clay's right to a seat in the Senate was never even challenged, let alone did the question even arise at all.
Thus, it's erroneous to assume that, b/c Clay was first elected to (& sat in) the Senate when he was under age, a precedent has been established under which we can reasonably act in the future, not least due to the fact that a newer, more relevant precedent has already been set since the days of Clay: in November 1934, at age 29, Rush Holt Sr. was elected to the Senate, but he didn't take his seat until after his 30th birthday in June 1935.
So, if AOC were (somehow) elected VP in 2020, she'd definitely be prohibited from taking office until her 35th birthday, nearly at the end of the term in 2024.
It's happened more recently. Joe Biden (born November 1942) was 29 when elected to the Senate but turned 30 before he was sworn in on January 5. The Constitution is explicit that the House and Senate are the judges of their respective members' qualifications, so I think as long as the member was in the majority party, there'd be nothing to stop the seating of an underage member of Congress.
